Model Formulation: Figure REF  shows our model architecture, which is adapted from [1]}.
The joint distribution
\(p_\theta (\textbf {X}^{\scriptsize {\textrm {}}}, \textbf {z}^{\scriptsize {\textrm {art}}}, \textbf {z}^{\scriptsize {\textrm {dyn}}}|\textbf {Y}^{\scriptsize {\textrm {onset}}}, \textbf {c}^{\scriptsize {\textrm {art}}}, \textbf {c}^{\scriptsize {\textrm {dyn}}}) = p_\theta (\textbf {X}^{\scriptsize {\textrm {}}}|\textbf {Y}^{\scriptsize {\textrm {onset}}}, \textbf {z}^{\scriptsize {\textrm {art}}}, \textbf {z}^{\scriptsize {\textrm {dyn}}}) p_\theta (\textbf {z}^{\scriptsize {\textrm {art}}}|\textbf {c}^{\scriptsize {\textrm {art}}})p_\theta (\textbf {z}^{\scriptsize {\textrm {dyn}}}|\textbf {c}^{\scriptsize {\textrm {dyn}}})\) ,
where \(\theta \)  refers to parameters of the generation network.
Both the prior distributions \(p_\theta (\textbf {z}^{\scriptsize {\textrm {art}}})\)  and \(p_\theta (\textbf {z}^{\scriptsize {\textrm {dyn}}})\)  are Gaussian mixtures of two components.
A variational distribution \(q_\phi (\textbf {z}^{\scriptsize {\textrm {}}}|\textbf {X}^{\scriptsize {\textrm {}}})\)  is introduced to approximate the true posterior,
where \(\phi \)  refers to parameters of the inference network.
The model is trained to optimize the evidence lower bound:
